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Problem Solving By Searching

Problem Solving By Searching . Introduction Solutions and Performance Uninformed Search Strategies Avoiding Repeated States/Looping Partial Information Summary. Introduction. Let’s review a goal-based agent called a “problem-solving agent” They have two characteristics:

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Problem Solving By Searching

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  1. Problem Solving By Searching • Introduction • Solutions and Performance • Uninformed Search Strategies • Avoiding Repeated States/Looping • Partial Information • Summary

  2. Introduction • Let’s review a goal-based agent called a • “problem-solving agent” • They have two characteristics: • Find sequences of actions to reach a goal. • They are uninformed.

  3. Preliminaries • We need to define two things: • Goal Formulation • Define objectives • Problem Formulation • Define actions and states

  4. Problem Formulation • Four components: • The initial state • Actions (successor function) • Goal test • Path Cost

  5. Example

  6. Other Examples • Toy Problems: • Vacuum World • 8-puzzle • 8-queens problem

  7. Figure 3.3

  8. Figure 3.5

  9. Other Examples • Real Problems • Route-Finding Problem • Robot Navigation • Automatic Assembly Sequencing • Protein Design • Internet Searching

  10. Problem Solving By Searching • Introduction • Solutions and Performance • Uninformed Search Strategies • Avoiding Repeated States • Partial Information • Summary

  11. Solutions • We search through a search tree • We expand new nodes to grow the tree • There are different search strategies • Nodes contain the following: • state • parent node • action • path cost • depth

  12. Search Tree Initial state Expanded nodes

  13. Performance • Four elements of performance: • Completeness (guaranteed to find solution) • Optimality (optimal solution?) • Time Complexity • Space Complexity

  14. Performance • Complexity requires three elements: • Branching factor b • Depth of the shallowest node d • Maximum length of any path m

  15. Problem Solving By Searching • Introduction • Solutions and Performance • Uninformed Search Strategies • Avoiding Repeated States • Partial Information • Summary

  16. Breadth-First Search • Root is expanded first • Then all successors at level 2. • Then all successors at level 3, etc. • Properties: • Complete (if b and d are finite) • Optimal (if path cost increases with depth) • Cost is O(bd+1)

  17. Search

  18. Uniform-Cost Search • Like breadth-first search • Expand node with lowest path cost. • Properties: • Complete (if b and d are finite) • Optimal (if path cost increases with depth) • Cost is O(b c*/e) • Could be worse than breadth first search

  19. Search

  20. Depth-First Search • Expand the deepest node at the bottom • of the tree. • Properties: • Incomplete • suboptimal • Space complexity is only O(bm) Backtracking even does better spacewise: O(m) Only store the nodes on the current path including their unexpanded sibling nodes

  21. Search

  22. Depth-Limited • Like depth-first search but with • depth limit L. • Properties: • Incomplete (if L < d) • nonoptimal (if L > d) • Time complexity is O(bL) • Space complexity is O(bL)

  23. Iterative Deepening • A combination of depth and breadth-first • search. • Gradually increases the limit L • Properties: • Complete (if b and d are finite) • Optimal if path cost increases with depth • Time complexity is O(bd)

  24. Search

  25. Bidirectional Search • Run two searches – one from the initial state • and one backward from the goal. • We stop when the two searches meet. • Motivation: • Time complexity: (b d/2 + b d/2 ) < b d Searching backwards not easy.

  26. Figure 3.16

  27. Problem Solving By Searching • Introduction • Solutions and Performance • Uninformed Search Strategies • Avoiding Repeated States/Looping • Partial Information • Summary

  28. Avoiding Looping & Repeated States • Use a list of expanded states; non-expanded • states (open and close list) • Use domain specific knowledge • Use sophisticated data structures to find • already visited states more quickly. • Checking for repeated states can be quite • expensive and slow down the search alg.

  29. Problem Solving By Searching • Introduction • Solutions and Performance • Uninformed Search Strategies • Avoiding Repeated States • Partial Information • Summary

  30. Partial Information • Knowledge of states or actions is incomplete. • Sensorless problems • Contingency Problems • Exploration Problems

  31. Figure 3.21 Goal State Goal State

  32. Problem Solving By Searching • Introduction • Solutions and Performance • Uninformed Search Strategies • Avoiding Repeated States • Partial Information • Summary

  33. Summary • To search we need goal and problem • formulation. • A problem has initial state, actions, goal test, • and path function. • Performance measures: completeness, • optimality, time and space complexity.

  34. Summary • Uninformed search has no additional • knowledge of states: breadth and depth-first • search, depth-limited, iterative deepening, • bidirectional search. • In partially observable environments, one • must deal with uncertainty and incomplete • knowledge.

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